The first and second nearest neighbour Cr3+ pairs in ruby

The irreducible representations of the states of the first and second nearest neighbour Cr³⁺ pairs in ruby were deduced from the known states of the single ions by the group theoretical method of induction. The summetry selection rules and polarizations for electric dipole radiation are discussed.Supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 65 Frankfurt-Darmstadt.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

On the mass spectrum of the 2+1 gauge-Higgs lattice quantum field theory

We investigate the mass spectrum of a 2+1 lattice gauge-Higgs quantum field theory with Wilson action A _P+A _H, whereA _P(A _H) is the gauge (gauge-Higgs) interaction. We determine the complete spectrum exactly for all , >0 by an explicit diagonalization of the gauge invariant transfer matrix in the approximation that the interaction terms in the spatial directions are omitted; all gauge invariant eigenfunctions are generated directly. For fixed momentum the energy spectrum is pure point and disjoint simple planar loops and strings are energy eigenfunctions. However, depending on the gauge group and Higgs representations, there are bound state energy eigenfunctions not of this form. The approximate model has a rich particle spectrum with level crossings and we expect that it provides an intuitive picture of the number and location of bound states and resonances in the full model for small , >0. We determine the mass spectrum, obtaining convergent expansions for the first two groups of masses above the vacuum, for small , and confirm our expectations.Research partially supported by CNPq, Brasil     

Metastable states in the van der Waals-Maxwell theory

A slight modification of the recent Penrose and Lebowitz treatment of thermodynamic metastable states is presented. For the case of periodic boundary conditions, this modification allows the condition of metastability to be extended to all the metastable states in the van der Waals-Maxwell theory of the liquid-vapor phase transition, that is, for all states satisfyingf ₀()+1/2 ²>f(, 0+) andf₀()+x>0 wheref(, 0+) is the (stable) Helmholtz free energy density of the generalized van der Waals-Maxwell theory andf ₀() is the Helmholtz free energy density of a reference system with no long-range interaction, is a mean field-type term arising from a long-range Kac interaction, is the overall mean particle density, andx is any positive number. For the case of rigid-wall boundary conditions, a more restrictive condition is placed onx.     

Interaction of conduction electrons in solids

It is shown that the influence of the interaction of conduction electrons with phonons can be partly included in the potential energy of their interaction. The effective potential energy found is used to study the possibility of the existence of bound states of two electrons in polar, homopolar and metallic crystals.     

Numerical estimate of the phase diagram of finite ANNNI chains in transverse field

We have estimated numerically the phase diagram of a one dimensional spin 1/2 quantum Ising model with competing nearest and next nearest neighbour interactions in presence of a transverse field. The method essentially is to diagonalise exactly the Hamiltonian for finite (10 spins) open chains and calculate the spin-spin correlations from the ground state eigenvector. The results obtained confirm the transition between ferromagnetic and paramagnetic phases for <0.5 and between antiphase and paramagnetic phase for >0.5. ( is the ratio of next nearest and nearest neighbour interactions.) The results perhaps indicate furthermore that (i) there is a disorder line passing through =0.5; (ii) the zero point quantum fluctuations destroy the order near =0.5 as the transverse field is switched on; and (iii) there is probably also a floating phase with slowly decayling correlation near the order-disorder phase boundary for >0.5.     

Energy relaxation in disordered charge and spin density waves

We investigate collective effects in the strong pinning model of disordered charge and spin density waves (CDWs and SDWs) in connection with heat relaxation experiments. We discuss the classical and quantum limits that contribute to two distinct contribution to the specific heat (a Cv T-2 contribution and a Cv T contribution respectively), with two different types of disorder (strong pinning versus substitutional impurities). From the calculation of the two level system energy splitting distribution in the classical limit we find no slow relaxation in the commensurate case and a broad spectrum of relaxation times in the incommensurate case. In the commensurate case quantum effects restore a non vanishing energy relaxation, and generate stronger disorder effects in incommensurate systems. For substitutional disorder we obtain Friedel oscillations of bound states close to the Fermi energy. With negligible interchain couplings this explains the power-law specific heat Cv T observed in experiments on CDWs and SDWs combined to the power-law susceptibility (T)T-1+ observed in the CDW o-TaS3.     

The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

A Relativistic Schrödinger-like Equation for a Photon and Its Second Quantization

Maxwell's equations are formulated as a relativistic Schrödinger-like equation for a single photon of a given helicity. The probability density of the photon satisfies an equation of continuity. The energy eigenvalue problem gives both positive and negative energies. The Feynman concept of antiparticles is applied here to show that the negative-energy states going backward in time (t –t) give antiphoton states, which are photon states with the opposite helicity. For a given mode, properties of a photon, such as energy, linear momentum, total angular momentum, orbital angular momentum, and spin are equivalent in both classical electromagnetic field theory and quantum theory. The single-photon Schrödinger equation is field (or second) quantized in a gauge-invariant way to obtain the quantum field theory of many photons. This approach treats the quantization of electromagnetic radiation in a way that parallels the quantization of material particles and, thus, provides a unified treatment.     

Melnikov's criterion for nondifferentiable weak-noise potentials

The stationary probability density of Fokker-Planck models with weak noise is asymptotically of the form exp[–1 /(q)]. If is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, has the properties of a Liapounov function, and can be used, e.g., as a thermodynamic potential in nonequilibrium steady states. We consider systems having several attractors and show, by applying Melnikov's method to the associated Hamiltonian, that in general is not differentiable. A small perturbation of a model with differentiable leads to a nondifferentiable . The method is illustrated on a model used in the treatment of the unstable mode in a laser.     

The free energy of a class of Hopfield models

We show that in the limitp ,N 0,=p/N 0 the limit free energy of the Hopfield model equals in probability the Curie-Weiss free energy. We prove also that the free energy of the Hopfield model is self-averaging for any finite .     

Local energy flux and the refined similarity hypothesis

In this paper we demonstrate the locality of energy transport for incompressible Euler equations both in space and in scale. The key to the proof is the proper definition of a local subscale flux, _t (r), which is supposed to be a measure of energy transfer to length scales <l at the space point r. Kraichnan suggested that for such a quantity the refined similarity hypothesis will hold, which Kolmogorov originally assumed to hold instead for volume-averaged dissipation. We derive a local energy-balance relation for the large-scale motions which yields a natural definition of such a subscale flux. For this definition a precise form of the refined similarity hypothesis is rigorously proved as a big-O bound. The established estimate is _t (r)=O(l _3h-1) in terms of the local Hölder exponenth at the point r, which is also the estimate assumed in the Parisi-Frisch multifractal model. Our method not only establishes locality of energy transfer, but it also clarifies the physical reason that convection effects, which naively violate locality, do not contribute to the subscale flux. In fact, we show that, as a consequence of incompressibility, such effects enter into the local energy balance only as the divergence of a spatial current. Therefore, they describe motion of energy in space and cancel in the integration over volume. We also discuss theorems of Onsager, Eyink, and Constantinet al. on energy conservation for Euler dynamics, particularly to explain their relation with the Parisi-Frisch model. The Constantinet al. proof may be interpreted as giving a bound on the total flux, _t =d ^d r _t (r), of the form _t (r)=O(l _z3h-1), wherez ₃ is the third-order scaling exponent (or Besov index), in agreement with the multifractal model. Finally, we discuss how the local estimates are related to the results of Caffarelli-Kohn-Nirenberg on partial regularity for solutions of Navier-Stokes equations. They provide some heuristic support to a scenario proposed recently by Pumir and Siggia for singularities in the solutions of Navier-Stokes with small enough viscosity.     

NESS theory of random steady states

A theory is presented for the properties of random steady states based upon a generalization of existing theories of nonrandom steady states. A sample calculation is presented for the energy cascade in a weakly stirred system. The theory introduces multivariable time correlation functions, and a new method for evaluating such objects is also given.Research supported by NSF grant No. CHE78-09704.Dreyfus Teacher-Scholar.     

Monochromatization of synchrotron radiation for nuclear resonant scattering experiments

An introduction to monochromatization of synchrotron radiation in the energy range of 5–30 keV is presented for applications involving nuclear resonant scattering. The relevant relationships of the dynamical theory of Xray diffraction are used to explain basic concepts of monochromatization. These relations are combined with raytracing techniques to design highenergyresolution monochromators. Transmissionoptimized and energyresolutionoptimized designs that achieve high energy resolutions (10⁶)< E/E < 10⁸) are discussed separately. Practical silicon monochromators of both types are presented for a variety of nuclear resonances in this energy range.     

On some frequent but controversial statements concerning the Einstein-Podolsky-Rosen correlations

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that the first in time of two correlated measurements instantaneously collapses the other subsystem; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning process and becoming, and his Whiteheadean concept of an advancing front, I object that they belong to factlike macrophysics, and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only look compatible at the macrolevel. Therefore, the classical objectivity must yield in favor of intersubjectivity. Only the macroscopic preparing and measuring devices have factlike objectivity; the transition of the quantal system takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in creative process, the elementary forms of which should be termed precognition or psychokinesis—respectively symmetric to the factlike taboos that we can neither know into the future nor act into the past. It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating low level psychokinesis—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of maya is the (rare) occurrence of paranormal phenomena. The essential severance between act and potentia is not a spacelike advancing front, but the out of and the into factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

КОРРЕКЦИОННЫЕ ФАКТО РЫ ПРИ АБСОЛЮТНОЙ ДОЗ ИМЕТРИИ ПЛОСКИХ ИСТОЧНИКОВβ-ИЗЛУЧЕНИЯ С ПОМОЩЬЮ СЧЕТЧИКА ГЕЙГЕРА-МЮЛ ЛЕРА

n n, n , .     

Large deviations for the 2D ising model: A lower bound without cluster expansions

We show that a lower large-deviation bound for the block-spin magnetization in the 2D Ising model can be pushed all the way forward toward its correct Wulff value for all >_c.     

Electronic structure of amorphous Nb1-x Si x films studied by X-ray emission and X-ray photoelectron spectroscopy

We present valence band spectra of the amorphous system Nb_1–x Si _x (0.2x0.8), of bcc-Nb and of a-Si obtained by X-ray photoelectron spectroscopy (XPS, Al K) and X-ray emission spectroscopy (XES, Si K-emission bands). The samples were prepared as thin films by sputtering. The origin of all prominent spectral features was identified and consistently correlated to Si 3s-, Si 3p-and Nb 4d-derived states. The Nb4d-Si3p coupling is stable in binding energy over a wide concentration range. There is strong experimental evidence that the short range order changes considerably within the concentration interval 0.4x0.7, whereas the partial density of states of the Si 3p-electrons is clearly altered in the small concentration range 0.50x0.57.